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Neither free outer cell rule is promoted, decided by coverage rather than by
grid accuracy (#331). 200 seeds at each of three resolutions, all
four arms post-processed off one solve per seed so the comparison is paired.
The placement rule contracts the atom set instead of correcting it -- its sigma_1 width ratio is 0.4776 / 0.5840 / 0.4465, flat in resolution rather
than decaying, because each atom moves a share of its own box and that share
does not shrink as the boxes do -- and covers 128 / 129 / 118 of 200 against
the shipped 200 / 200 / 200. The mass rule never moves a sigma_1 trial and
widens that interval by 4.1% to 9.8%.
The decisive number is that the placement rule is CLOSER to the fine grid and
still loses: per-seed distance to the same seed's 1296-cell width is 0.3576
against the shipped 0.4194, and it gives up 72 seeds of coverage. The two
error directions do not cost the same, so a rule selected on distance to a
finer grid can be selected against on calibration. That is what the issue was
opened to establish. On the fixed effects coverage cannot separate the arms at
any affordable N (1 discordant seed of 200 on the intercept, 0 on the slope),
so only the width is a measurement there; the seed count was chosen from an
exact sign-test power calculation rather than from the deficit the
pre-gcol33/tulpa#332 fixture appeared to carry.
A two-dimensional pre-refinement descriptor does not select a per-cell
correction either (#333), measured by one-cell intervention on the
global read over 2520 cells from 216 fits. The mass and location descriptors
do separate once the box truncation is applied (Spearman 0.8496 against 0.9495
in the unbounded metric), but the best label per quadrant buys +0.0000 over
the single best label overall in 23 of 30 scored combinations, and where the
direction is strongest it runs backwards. The issue's central hypothesis is
refuted: the four- and five-level grids occupy statistically indistinguishable
regions of the plane.
Those three negative results have one mechanism and the header now says so
once rather than leaving it to be rediscovered: posterior mass dominates every
level of this grid. A second, structural reason is recorded alongside it --
the outer read is a weighted quantile, which couples cells through ordering
and cumulative mass, so summed per-cell improvements exceed the whole-grid
improvement by 8.48x to 68.58x and at five levels carry opposite signs. A
perfect per-cell classifier would still not compose into a grid rule.
A declined outer cell-mass or barycentre axis says which gate it fell at
(#334): boundary, no_factor, cancellation and, for the
barycentre, out_of_box, tallied per cell on both sides of the refinement
gate. n_axes_declined is unchanged and rides alongside. The reasons are
taken at the same constants that already gate the refusals rather than
re-derived afterwards, and each one is triggered by a real fixture rather than
shipped as an unobserved string -- out_of_box turning out to be unreachable
through the closed form by construction, since its error bound sits under the
in-box slack.